The many and various schools of Hinduism have one thing in common, acceptance of the Vedas as supreme teaching, even if there are many differing interpretations on exactly what the Vedas say.
In Buddhism, certain ideas were held as the basic, fundamental aspects of the religion, such as the Four Noble Truths, the Noble Eightfold Path, the Three Marks of Existence/Four Dharma Seals, and the Three Refuges and Five Precepts. Since the debate is about anatta, which is one of the Three Marks/Four Seals, it's important to note that it is one of the basic teachings of Buddhism, and trying to force it to say something it doesn't takes away from buddhadharma.
This is one of the reasons why syncretism is hard to do, especially when Buddhism is involved. Anatta is unique to Buddhism, to the best of my knowledge, and it doesn't really fit well with other religions. It's not an easy teaching to either accept or understand, but it is what it is. While I don't have a problem with those who want to practice Buddhism and another religion simultaneously, saying that Buddhism does not teach something that it does, based on nothing more than one's own ideas and beliefs, is disingenuous. It would be the same if I tried to make people believe that Advaita teaches atheism, or Bakhti teaches there is no god or soul. It simply doesn't work that way.